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1 Pure Mathematics

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Question 1407

It is given that g(x)=4x3−8x2−35x+75g(x) = 4x^3 - 8x^2 - 35x + 75g(x)=4x3−8x2−35x+75

a.

Demonstrate, by evaluating g g\,g at a suitable integer, that (x+3)(x+3)(x+3) divides g(x)g(x)g(x) exactly.

[2]
b.

Hence show that g(x)g(x)g(x) can be written in the form g(x)=(x+3)(ax+b)2g(x) = (x + 3)(ax + b)^2g(x)=(x+3)(ax+b)2, where a a\,a and b b\,b are constants to be found.

[4]
Markscheme

1 Pure Mathematics Questions

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